Coronary artery disease is the leading cause of morbidity and mortality worldwide. Selected patients with obstructive coronary artery disease benefit from revascularization with percutaneous coronary intervention (PCI) or coronary artery bypass graft (CABG) surgery. Many (but not all) studies have demonstrated increased survival and greater freedom from adverse cardiovascular events after complete revascularization (CR) than after incomplete revascularization (ICR) in patients with multivessel disease. However, achieving CR after PCI or CABG surgery might not be feasible owing to patient comorbidities, anatomical factors, and technical or procedural considerations. These factors also mean that comparisons between CR and ICR are subject to multiple confounders and are difficult to understand or apply to real-world clinical practice. In this Review, we summarize and critically appraise the evidence linking various types of ICR to adverse outcomes in patients with multivessel disease and stable ischaemic heart disease, non-ST-segment elevation acute coronary syndrome or ST-segment elevation myocardial infarction, with or without cardiogenic shock. In addition, we provide practical recommendations for revascularization in patients with high-risk multivessel disease to optimize their long-term clinical outcomes and identify areas requiring future clinical investigation.